Low-frequency vibrational modes usually emerge due to hindered or near-free rotations around a single bond within a molecule. The harmonic approximation is problematic for such internal rotations and yields an infinite vibrational entropy Svib in the limit of vanishing frequencies.
To fix this issue, Grimme
460
Chem. Eur. J
(2012),
18,
pp. 9955.
Link
proposed to enforce a finite vibrational entropy by interpolating between the entropy of the free rotor SFR and the harmonic vibrational entropy SHO as
| Svib(νi)=(1-ω(νi))SFR(νi)+ω(νi)SHO(νi), | (10.42) |
where
| ω(νi)=11+(ν0/νi)α | (10.43) |
is the damping function of Chai and Head-Gordon,
207
Phys. Chem. Chem. Phys.
(2008),
10,
pp. 6615.
Link
with α and ν0 as fixed parameters.
It is used as a weighting function and allows for a smooth transition from the free rotor entropy at small frequencies
to the harmonic vibrational entropy for frequencies νi above the cutoff ν0.
This was later extended to interpolate the vibrational enthalpy contributions between a free rotor
HFR and a harmonic oscillator HHO with zero-point vibrational energy
HZPVE, as
776
J. Phys. Chem. C
(2015),
119,
pp. 1840.
Link
| Hvib(νi)=[1-ω(νi)]HFR(νi)+ω(νi)[HHO(νi)+HZPVE(νi)]. | (10.44) |
This again reduces the error associated with treating translational and rotational degrees of freedom as low-frequency vibrations, which is especially important for the adsorption or association of larger molecules. This procedure is known as the quasi-rigid-rotor-harmonic-oscillator (qRRHO) approach.
The qRRHO scheme is the default in Q-Chem, and all thermodynamic quantities are printed for the RRHO (without interpolations) and qRRHO schemes at standard temperature and pressure (298.15 K and 1.00 atm). To change the latter, the user can specify an $isotopes section (see examples and Section 10.7.2 for details). α and ω0 for both interpolator functions can be modified through QRRHO_ALPHA and QRRHO_OMEGA_CUTOFF respectively.
QRRHO_ALPHA
QRRHO_ALPHA
Specifies the exponent in the damping function of Chai and Head-Gordon,
used for interpolating the vibrational enthalpy and entropy in the qRRHO scheme.
Specify MRRHO_ALPHA to change the exponent for the entropy interpolation separately.
TYPE:
INTEGER
DEFAULT:
4
OPTIONS:
α
Dimensionless interpolator exponent used in the qRRHO scheme.
RECOMMENDATION:
Use the default.
QRRHO_OMEGA_CUTOFF
QRRHO_OMEGA_CUTOFF
Sets the frequency cutoff in the Chai-Head-Gordon damping function for interpolating the vibrational enthalpy
and entropy in the qRRHO scheme. Specify MRRHO_OMEGA_CUTOFF to change the frequency cutoff
for the entropy interpolation separately.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
ω0
Interpolator cutoff frequency used in the qRRHO scheme in cm-1.
RECOMMENDATION:
Use the default.
Example 10.31 Harmonic vibrational analysis at the HF/3-21G level of theory, where the thermodynamic properties for RRHO and qRRHO are printed at 298.15 K and 1.00 atm.
$molecule 0 1 C 1.682185104800 0.240320237000 0.000000000000 O 0.894276382600 1.089998584000 0.000000000000 O 2.480949717100 -0.590833069200 0.000000000000 C -1.682185094800 -0.240320333400 0.000000000000 O -0.894276273900 -1.089998812500 0.000000000000 O -2.480949835800 0.590833394100 0.000000000000 $end $rem JOBTYPE opt METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end @@@ $molecule read $end $rem JOBTYPE freq METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end
Example 10.32 Harmonic vibrational analysis at the HF/3-21G level of theory, where the thermodynamic properties for RRHO and qRRHO are printed at standard temperature and pressure as well as two additional temperatures (273.15 K and 313.15 K). Please see Section 10.7.2 for further details on the $isotopes section.
$molecule 0 1 C 1.682185104800 0.240320237000 0.000000000000 O 0.894276382600 1.089998584000 0.000000000000 O 2.480949717100 -0.590833069200 0.000000000000 C -1.682185094800 -0.240320333400 0.000000000000 O -0.894276273900 -1.089998812500 0.000000000000 O -2.480949835800 0.590833394100 0.000000000000 $end $rem JOBTYPE opt METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end @@@ $molecule read $end $rem JOBTYPE freq METHOD hf BASIS 3-21G ISOTOPES true INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end $isotopes 2 1 0 273.15 1.0 0 313.15 1.0 $end